An ideal gas, Cv = 52R, is expanded adiabatically against a constant pressure of 1 atm until it doubles in volume. If the initial temperature and pressure is 298 K and 5 atm, respectively then the final temperature is K (nearest integer). [ cv is the molar heat capacity at constant volume]
Answer
274
Solution
Adiabatic (q = 0), irreversible: U = w ⇒ nCv(T2 - T1) = -Pext(V2 - V1)
∵ V2 = 2V1 ⇒ V2 - V1 = V1 = nRT1P1
⇒ 52R(T2 - 298) = -1 R 2985
⇒ T2 - 298 = - 2 29825 = -23.84
∴ T2 = 274.16 K 274 K
Answer: 274